Calculator Online

Home AI Chat AI Math Solver

NEW

Tools ▾ Category ▾

Pricing Sign In

Calculator Online

Your Result is copied!

Golden Ratio Calculator

Select the calculation type and fetch the required parameters to determine the golden ratio using this golden ratio calculator.

Calculation With:

Shorter section (A):

m ▾

Related

Golden Ratio Calculator

The online golden ratio calculator allows you to compute proportional values based on the golden ratio. You can enter the shorter segment, longer segment, or the total length to instantly determine the remaining measurements. Before using the tool, let’s review the concept behind the golden ratio.

What is the Golden Ratio?

“Two quantities are in the golden ratio if the ratio of the whole to the larger part is equal to the ratio of the larger part to the smaller part.”

This special proportion is represented by the Greek letter φ (phi).

Golden ratio illustration

Golden Ratio Formula

Mathematically, the golden ratio is defined as:

\( \phi = \frac{A + B}{A} = \frac{A}{B} \)

Its exact and approximate values are:

\( \phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887 \)

Formulas for Each Segment

Longer section (A): \( A = B \times \phi \)
Shorter section (B): \( B = \frac{A}{\phi} \)
Total length: \( A + B = A\phi \)

Golden Rectangle

“A rectangle whose side lengths follow the golden ratio is known as a golden rectangle.”

Golden rectangle diagram

Notable properties of a golden rectangle include:

If a square is removed from it, the remaining rectangle is still golden.
Repeating this process forms a logarithmic spiral often seen in nature.

Fibonacci Sequence

“The Fibonacci sequence is a series of numbers where each term equals the sum of the two preceding terms.”

Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

Connection Between Fibonacci Numbers and the Golden Ratio

The ratio of consecutive Fibonacci numbers gradually approaches the golden ratio.

Step	A	B	B/A
1	2	3	1.5
2	3	5	1.666
3	5	8	1.6
4	8	13	1.625
5	233	377	1.618

Examples of Golden Ratio Calculations

Example 1: If the shorter section B = 4 cm, find the longer section.

\( A = 4 \times 1.618 = 6.472 \, \text{cm} \)

Example 2: If the longer section A = 10 cm, find the shorter section.

\( B = \frac{10}{1.618} \approx 6.18 \, \text{cm} \)

How the Golden Ratio Calculator Works

Follow these steps to use the calculator:

Select whether you know the longer section, shorter section, or total length.
Enter the given value in the input field.
Click Calculate to generate results.

The calculator provides:

Longer segment (A)
Shorter segment (B)
Total length (A + B)
Golden ratio value (φ ≈ 1.618)

Frequently Asked Questions

Why is the golden ratio important?

It is widely regarded as visually harmonious and appears in art, architecture, design, and natural patterns.

Does the Fibonacci sequence relate to the golden ratio?

Yes. As Fibonacci numbers increase, the ratio between consecutive terms approaches 1.618, the golden ratio.

Is the golden ratio an irrational number?

Yes. Its decimal expansion continues infinitely without repeating.

What is the golden angle?

The golden angle is approximately \(137.5^\circ\), commonly observed in plant growth patterns.

Who first described the golden ratio?

The term “golden ratio” was popularized by the German mathematician Martin Ohm in the 19th century.

Conclusion

The golden ratio plays a significant role in mathematics, design, architecture, and nature. Using a golden ratio calculator ensures precise and quick proportional calculations for practical and creative applications.

References

Related

Calculator Online

Get the ease of calculating anything from the source of calculator online

Links

Home Conversion Calculator About Calculator Online Blog Hire Us Knowledge Base Sitemap Sitemap Two

Support

Email us at